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For my project I need to reverse a table-based CRC16 because I have to change some data without changing the CRC.

My problem is to reverse the look up table.

I found some other solutions to reverse the look up table, but not for my CRC table.

#define SIZE_OF_CRC_TABLE 256u
static const uint16_t crc_polynom = 0x1021;

void Compute_CRCTables(uint16_t *CRCTable_forward, uint16_t *CRCTable_reverse) {
    uint16_t result_forward, result_reverse;
    int i, j;

    for (i = 0; i < SIZE_OF_CRC_TABLE; i++) {
        result_forward = (uint16_t) i << 8;
        result_reverse = i;

        for (j = 0; j < 8; j++) {
            /* ---- forward ---- */
            if (result_forward & 0x8000) {
                result_forward = (result_forward <<= 1) ^ crc_polynom;
            }
            else {
                result_forward = result_forward <<= 1;
            }

            /* ---- reverse --- */
            if ((result_reverse & 0x1) != 0) {
                result_reverse = ((result_reverse ^ crc_polynom) >> 1) | 1;
            }
            else {
                result_reverse = result_reverse >>= 1;
            }
        }
        CRCTable_forward[i] = result_forward;
        CRCTable_reverse[i] = result_reverse;
    }
}

CRC table:

0x   0u, 0x1021u, 0x2042u, 0x3063u, 0x4084u, 0x50A5u, 0x60C6u, 0x70E7u,
0x8108u, 0x9129u, 0xA14Au, 0xB16Bu, 0xC18Cu, 0xD1ADu, 0xE1CEu, 0xF1EFu,
0x1231u, 0x 210u, 0x3273u, 0x2252u, 0x52B5u, 0x4294u, 0x72F7u, 0x62D6u,
0x9339u, 0x8318u, 0xB37Bu, 0xA35Au, 0xD3BDu, 0xC39Cu, 0xF3FFu, 0xE3DEu,
0x2462u, 0x3443u, 0x 420u, 0x1401u, 0x64E6u, 0x74C7u, 0x44A4u, 0x5485u,
0xA56Au, 0xB54Bu, 0x8528u, 0x9509u, 0xE5EEu, 0xF5CFu, 0xC5ACu, 0xD58Du,
0x3653u, 0x2672u, 0x1611u, 0x 630u, 0x76D7u, 0x66F6u, 0x5695u, 0x46B4u,
0xB75Bu, 0xA77Au, 0x9719u, 0x8738u, 0xF7DFu, 0xE7FEu, 0xD79Du, 0xC7BCu,
0x48C4u, 0x58E5u, 0x6886u, 0x78A7u, 0x 840u, 0x1861u, 0x2802u, 0x3823u,
0xC9CCu, 0xD9EDu, 0xE98Eu, 0xF9AFu, 0x8948u, 0x9969u, 0xA90Au, 0xB92Bu,
0x5AF5u, 0x4AD4u, 0x7AB7u, 0x6A96u, 0x1A71u, 0x A50u, 0x3A33u, 0x2A12u,
0xDBFDu, 0xCBDCu, 0xFBBFu, 0xEB9Eu, 0x9B79u, 0x8B58u, 0xBB3Bu, 0xAB1Au,
0x6CA6u, 0x7C87u, 0x4CE4u, 0x5CC5u, 0x2C22u, 0x3C03u, 0x C60u, 0x1C41u,
0xEDAEu, 0xFD8Fu, 0xCDECu, 0xDDCDu, 0xAD2Au, 0xBD0Bu, 0x8D68u, 0x9D49u,
0x7E97u, 0x6EB6u, 0x5ED5u, 0x4EF4u, 0x3E13u, 0x2E32u, 0x1E51u, 0x E70u,
0xFF9Fu, 0xEFBEu, 0xDFDDu, 0xCFFCu, 0xBF1Bu, 0xAF3Au, 0x9F59u, 0x8F78u,
0x9188u, 0x81A9u, 0xB1CAu, 0xA1EBu, 0xD10Cu, 0xC12Du, 0xF14Eu, 0xE16Fu,
0x1080u, 0x  A1u, 0x30C2u, 0x20E3u, 0x5004u, 0x4025u, 0x7046u, 0x6067u,
0x83B9u, 0x9398u, 0xA3FBu, 0xB3DAu, 0xC33Du, 0xD31Cu, 0xE37Fu, 0xF35Eu,
0x 2B1u, 0x1290u, 0x22F3u, 0x32D2u, 0x4235u, 0x5214u, 0x6277u, 0x7256u,
0xB5EAu, 0xA5CBu, 0x95A8u, 0x8589u, 0xF56Eu, 0xE54Fu, 0xD52Cu, 0xC50Du,
0x34E2u, 0x24C3u, 0x14A0u, 0x 481u, 0x7466u, 0x6447u, 0x5424u, 0x4405u,
0xA7DBu, 0xB7FAu, 0x8799u, 0x97B8u, 0xE75Fu, 0xF77Eu, 0xC71Du, 0xD73Cu,
0x26D3u, 0x36F2u, 0x 691u, 0x16B0u, 0x6657u, 0x7676u, 0x4615u, 0x5634u,
0xD94Cu, 0xC96Du, 0xF90Eu, 0xE92Fu, 0x99C8u, 0x89E9u, 0xB98Au, 0xA9ABu,
0x5844u, 0x4865u, 0x7806u, 0x6827u, 0x18C0u, 0x 8E1u, 0x3882u, 0x28A3u,
0xCB7Du, 0xDB5Cu, 0xEB3Fu, 0xFB1Eu, 0x8BF9u, 0x9BD8u, 0xABBBu, 0xBB9Au,
0x4A75u, 0x5A54u, 0x6A37u, 0x7A16u, 0x AF1u, 0x1AD0u, 0x2AB3u, 0x3A92u,
0xFD2Eu, 0xED0Fu, 0xDD6Cu, 0xCD4Du, 0xBDAAu, 0xAD8Bu, 0x9DE8u, 0x8DC9u,
0x7C26u, 0x6C07u, 0x5C64u, 0x4C45u, 0x3CA2u, 0x2C83u, 0x1CE0u, 0x CC1u,
0xEF1Fu, 0xFF3Eu, 0xCF5Du, 0xDF7Cu, 0xAF9Bu, 0xBFBAu, 0x8FD9u, 0x9FF8u,
0x6E17u, 0x7E36u, 0x4E55u, 0x5E74u, 0x2E93u, 0x3EB2u, 0x ED1u, 0x1EF0u,

Reverse CRC table (wrong): 

0x   0u, 0x FEFu, 0x FFFu, 0x FEFu, 0x FDFu, 0x FEFu, 0x FFFu, 0x FEFu,
0x F9Fu, 0x FEFu, 0x FFFu, 0x FEFu, 0x FDFu, 0x FEFu, 0x FFFu, 0x FEFu,
0x F1Fu, 0x FEFu, 0x FFFu, 0x FEFu, 0x FDFu, 0x FEFu, 0x FFFu, 0x FEFu,
0x F9Fu, 0x FEFu, 0x FFFu, 0x FEFu, 0x FDFu, 0x FEFu, 0x FFFu, 0x FEFu,
0x E1Du, 0x FEFu, 0x FFFu, 0x FEFu, 0x FDFu, 0x FEFu, 0x FFFu, 0x FEFu,
0x F9Fu, 0x FEFu, 0x FFFu, 0x FEFu, 0x FDFu, 0x FEFu, 0x FFFu, 0x FEFu,
0x F1Fu, 0x FEFu, 0x FFFu, 0x FEFu, 0x FDFu, 0x FEFu, 0x FFFu, 0x FEFu,
0x F9Fu, 0x FEFu, 0x FFFu, 0x FEFu, 0x FDFu, 0x FEFu, 0x FFFu, 0x FEFu,
0x C19u, 0x FEFu, 0x FFFu, 0x FEFu, 0x FDFu, 0x FEFu, 0x FFFu, 0x FEFu,
0x F9Fu, 0x FEFu, 0x FFFu, 0x FEFu, 0x FDFu, 0x FEFu, 0x FFFu, 0x FEFu,
0x F1Fu, 0x FEFu, 0x FFFu, 0x FEFu, 0x FDFu, 0x FEFu, 0x FFFu, 0x FEFu,
0x F9Fu, 0x FEFu, 0x FFFu, 0x FEFu, 0x FDFu, 0x FEFu, 0x FFFu, 0x FEFu,
0x E1Du, 0x FEFu, 0x FFFu, 0x FEFu, 0x FDFu, 0x FEFu, 0x FFFu, 0x FEFu,
0x F9Fu, 0x FEFu, 0x FFFu, 0x FEFu, 0x FDFu, 0x FEFu, 0x FFFu, 0x FEFu,
0x F1Fu, 0x FEFu, 0x FFFu, 0x FEFu, 0x FDFu, 0x FEFu, 0x FFFu, 0x FEFu,
0x F9Fu, 0x FEFu, 0x FFFu, 0x FEFu, 0x FDFu, 0x FEFu, 0x FFFu, 0x FEFu,
0x 811u, 0x FEFu, 0x FFFu, 0x FEFu, 0x FDFu, 0x FEFu, 0x FFFu, 0x FEFu,
0x F9Fu, 0x FEFu, 0x FFFu, 0x FEFu, 0x FDFu, 0x FEFu, 0x FFFu, 0x FEFu,
0x F1Fu, 0x FEFu, 0x FFFu, 0x FEFu, 0x FDFu, 0x FEFu, 0x FFFu, 0x FEFu,
0x F9Fu, 0x FEFu, 0x FFFu, 0x FEFu, 0x FDFu, 0x FEFu, 0x FFFu, 0x FEFu,
0x E1Du, 0x FEFu, 0x FFFu, 0x FEFu, 0x FDFu, 0x FEFu, 0x FFFu, 0x FEFu,
0x F9Fu, 0x FEFu, 0x FFFu, 0x FEFu, 0x FDFu, 0x FEFu, 0x FFFu, 0x FEFu,
0x F1Fu, 0x FEFu, 0x FFFu, 0x FEFu, 0x FDFu, 0x FEFu, 0x FFFu, 0x FEFu,
0x F9Fu, 0x FEFu, 0x FFFu, 0x FEFu, 0x FDFu, 0x FEFu, 0x FFFu, 0x FEFu,
0x C19u, 0x FEFu, 0x FFFu, 0x FEFu, 0x FDFu, 0x FEFu, 0x FFFu, 0x FEFu,
0x F9Fu, 0x FEFu, 0x FFFu, 0x FEFu, 0x FDFu, 0x FEFu, 0x FFFu, 0x FEFu,
0x F1Fu, 0x FEFu, 0x FFFu, 0x FEFu, 0x FDFu, 0x FEFu, 0x FFFu, 0x FEFu,
0x F9Fu, 0x FEFu, 0x FFFu, 0x FEFu, 0x FDFu, 0x FEFu, 0x FFFu, 0x FEFu,
0x E1Du, 0x FEFu, 0x FFFu, 0x FEFu, 0x FDFu, 0x FEFu, 0x FFFu, 0x FEFu,
0x F9Fu, 0x FEFu, 0x FFFu, 0x FEFu, 0x FDFu, 0x FEFu, 0x FFFu, 0x FEFu,
0x F1Fu, 0x FEFu, 0x FFFu, 0x FEFu, 0x FDFu, 0x FEFu, 0x FFFu, 0x FEFu,
0x F9Fu, 0x FEFu, 0x FFFu, 0x FEFu, 0x FDFu, 0x FEFu, 0x FFFu, 0x FEFu,
Qeole
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Philipp Fu
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    Well you have some undefined behavior: `result_forward = (result_forward <<= 1) ^ crc_polynom;` is modifying `result_forward` twice. You need to replace `<<=` with `<<` here. Similarly, `result_forward = result_forward <<= 1;` should be `result_forward <<= 1;` and `result_reverse = result_reverse >>= 1;` should be `result_reverse >>= 1;` – Ian Abbott Jul 16 '19 at 10:35
  • You seem to have simply changed the order of some of the CRC computations and expect that to compute the inverse function. Instead, delete the computations for the reverse order and replace `CRCTable_reverse[i] = result_reverse;` with `CRCTable_reverse[result_forward] = i;`. – Eric Postpischil Jul 16 '19 at 10:49
  • Thanks @IanAbbott i correct my Code with your tipps. But the result is the same as before. – Philipp Fu Jul 16 '19 at 10:52

1 Answers1

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The poly needs to be reversed as well. This code avoids inner conditionals assuming two's complement math to generate 0x0000 or 0xffff as an and mask.

#define SIZE_OF_CRC_TABLE 256u
#define POLY_FWD 0x1021
#define POLY_RVS 0x8408

void Compute_CRCTables(uint16_t *CRCTable_forward, uint16_t *CRCTable_reverse) {
    uint16_t crc_fwd = 0;
    uint16_t crc_rvs = 0;
    int i, j;

    for (i = 0; i < SIZE_OF_CRC_TABLE; i++) {
        crc_fwd = ((uint16_t)i) << 8;
        crc_rvs = ((uint16_t)i) << 0;
        for (j = 0; j < 8; j++) {
            /* assumes two's complement math */
            crc_fwd = (crc_fwd << 1) ^ ((0 - (crc_fwd >> 15)) & POLY_FWD);
            crc_rvs = (crc_rvs >> 1) ^ ((0 - (crc_rvs &   1)) & POLY_RVS);
        }
        CRCTable_forward[i] = crc_fwd;
        CRCTable_reverse[i] = crc_rvs;
    }
}
rcgldr
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